Question

n a random sample of seven ​people, the mean driving distance to work was 19.5 miles and the standard deviation was 4.3 miles. Assume the population is normally distributed and use the​ t-distribution to find the margin of error and construct a 95​% confidence interval for the population mean mu. Interpret the results

Answer 1

Solution :

Given that,

= 19.5

s =4.3

n = Degrees of freedom = df = n - 1 =7 - 1 = 6

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,6 = 2.447 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.447 * (4.3 / 7)

= 3.98

The 95% confidence interval mean is,

- E < < + E

19.5 -3.98 < < 19.5+ 3.98

15.52 < < 23.48

( 15.52 , 23.48)

lower bound 15.52

upper bound 23.48